Page 109 - 摩擦学学报2025年第8期

第 8 期 肖科, 等: Lennard-Jones 势对硬涂层球-刚性平板间静摩擦行为的影响研究 1207

elastoplastic sphere, derived from the Lennard-Jones potential, are calculated with precision using a modified Derjaguin-
Muller-Toporov (DMT) adhesion model. This model is rigorously simulated and implemented within the Abaqus
environment through the user subroutine, taking into account real-time variations in the separation distance between the
elastoplastic sphere and the rigid plate during both normal loading and tangential displacement phases. This approach
ensures the accuracy and fidelity of the simulation, capturing the nuanced interactions at the interface. The validity and
reliability of the proposed adhesion model are thoroughly established by systematically comparing the simulation
outcomes with existing experimental data and models reported in the literature. The results of this investigation revealed
that at the microscale, specifically at the scale of surface roughness peaks, neglecting the contribution of adhesion can
lead to substantial errors in predicting the maximum static friction coefficient. This is especially pronounced under
conditions of low external normal loads, where the adhesive forces played a more dominant role. The study further
demonstrates that the maximum static friction coefficient initially exhibited a linear increase with the augmentation of
the hard coat thickness, eventually reaching an optimal peak value at a specific thickness, denoted by the dimensionless
ratio t/R = (t/R) m . Beyond this critical thickness, the maximum static friction coefficient was observed to decrease
following a hyperbolic cotangent function with further increases in coating thickness, eventually stabilizing at a certain
value. Additionally, the analysis highlighted that an increase in adhesive energy δ resulted in a corresponding increase in
the maximum static friction coefficient μ, although the overall trend in its variation with coating thickness remained
unchanged. The adhesive energy δ was shown to have a negligible impact on the critical thickness (t/R) m when the
material parameters remained constant. Finally, the study delved into the effects of dimensionless material parameters,
revealing that with an increase in the dimensionless parameter E co /E su , the influence of adhesive energy δ on the
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maximum static friction coefficient μ diminishes. In contrast, for a constant dimensionless load P , an increase in E co /Y co
was found to enhance the proportion of adhesive force relative to the total external normal load, thereby amplifying the
effect of adhesion energy on the static friction behavior. This comprehensive investigation provided valuable insights
into the complex interplay between coating thickness, adhesive forces, and material parameters in determining the static
friction characteristics at the microscale.
Key words: adhesive contact; LJ potential; elastoplastic contact; coefficient of static friction; hard coating

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摩擦是机械系统中造成能量耗散的重要原因之 Greenwood-Williamson (GW)模型 . 统计接触模型认
一 . 随着各类机电系统朝着高集成化和微小型化方向 为，表面之间的接触是通过单个粗糙峰接触行为的统
[1]
的发展，微尺度下的摩擦和磨损问题成为许多微型器 计特性来确定的. 对于存在涂层的接触表面，与GW粗
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件设计和应用的突出瓶颈. 例如，原子显微镜探针针 糙表面的接触模型类似，Chen等 假设涂层与基底具
[3]
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尖 和旋转微机械的微球轴承 等，因此，理解摩擦产 有相同的形貌，并且基底表面的微凸体可等效为球
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生机理并控制摩擦对提高设备的可靠性至关重要 . 形，涂层表面之间的接触实际是许多单独的涂层球相
涂层技术是最有效的表面改性技术之一 [5-6] ，因其 互接触. 因此，理解单个涂层球体在法向和切向联合
具有耐摩擦磨损、抵抗变形以及在微纳尺度下减小黏 载荷下的接触行为，是完善涂层表面接触和摩擦特性
着的优良性能 [7-9] 而被广泛应用. 例如，将硬涂层应用 理论的重要基础.
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于微电机中 ，可以增强电机的抗黏着性能并延长其 在纯法向载荷作用下，Keer等 得到了2个相同
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工作寿命；将涂层应用于硬盘驱动装置中的磁头或磁 涂层球接触界面处的应力分布，发现在相同接触半径
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[9]
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盘表面 ，以及微夹持装置执行器表面的末端 ，可以 下，较硬涂层产生较高界面法向应力. Garjonis等 确
提高硬盘驱动装置的整体读/写性能，或提高微夹持装 定了与载荷相关的相同接触涂层球体的等效弹性模
置对被夹持对象的有效释放性能. 涂层的厚度以及涂 量，由于这种有效模量受其载荷的影响，在实际应用
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层材料特性等对其摩擦学性能有直接影响 . 然而， 时存在一些不便. Chen等 研究了刚性平板与涂层球
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在实际应用中，确定这些重要参数仍主要依靠经验 . 在滑移接触条件下的塑性演化，并通过对第2次屈服
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因此，亟需建立1个理论预测模型，以减少经验设计带 起始时的临界值进行归一化 ，得到了弹塑性状态下
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来的偏差，从而更精确地调整表面的接触特性. 载荷-位移和接触面积-位移的通用无量纲关系 ，并
国内外学者就粗糙表面间的接触问题进行了大 建立了通用的弹塑性涂层球与刚性板的接触模型. 周
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量研究. 早期研究主要基于统计参数的接触模型，如 政 利用有限元法研究了涂层厚度与接触区应力分